Estimation of the probability density function of renewable power production using a hybrid method of minimum frequency and maximum entropy

The problem of randomized maximum entropy estimation for the probability density function of random model parameters with real data and measurement noises was formulated. This estimation procedure maximizes an information entropy functional on a set of integral equalities depending on the real data set. The technique of the Gâteaux derivatives is developed to solve this problem in analytical form. The probability density function estimates depend on Lagrange multipliers, which are obtained by balancing the model’s output with real data. A global theorem for the implicit dependence of these Lagrange multipliers on the data sample’s length is established using the rotation of homotopic vector fields. A theorem for the asymptotic efficiency of randomized maximum entropy estimate in terms of stationary Lagrange multipliers is formulated and proved. The proposed method is illustrated on the problem of forecasting of the evolution of the thermokarst lake area in Western Siberia.

Download Full-text

Extreme estimation of wind pressure with unimodal and bimodal probability density function characteristics: A maximum entropy model based on fractional moments

Journal of Wind Engineering and Industrial Aerodynamics ◽

10.1016/j.jweia.2021.104663 ◽

2021 ◽

Vol 214 ◽

pp. 104663

Author(s):

Wen Xie ◽

Peng Huang

Keyword(s):

Probability Density Function ◽

Probability Density ◽

Maximum Entropy ◽

Density Function ◽

Wind Pressure ◽

Maximum Entropy Model ◽

Entropy Model ◽

Model Based ◽

Fractional Moments

Download Full-text

Numerical Algorithms for Estimating Probability Density Function Based on the Maximum Entropy Principle and Fup Basis Functions

Entropy ◽

10.3390/e23121559 ◽

2021 ◽

Vol 23 (12) ◽

pp. 1559

Author(s):

Nives Brajčić Kurbaša ◽

Blaž Gotovac ◽

Vedrana Kozulić ◽

Hrvoje Gotovac

Keyword(s):

Probability Density Function ◽

Probability Density ◽

Maximum Entropy ◽

Density Function ◽

Moment Problem ◽

Statistical Power ◽

Maximum Entropy Principle ◽

Basis Functions ◽

Approximation Properties ◽

Hybrid Strategy

Estimation of the probability density function from the statistical power moments presents a challenging nonlinear numerical problem posed by unbalanced nonlinearities, numerical instability and a lack of convergence, especially for larger numbers of moments. Despite many numerical improvements over the past two decades, the classical moment problem of maximum entropy (MaxEnt) is still a very demanding numerical and statistical task. Among others, it was presented how Fup basis functions with compact support can significantly improve the convergence properties of the mentioned nonlinear algorithm, but still, there is a lot of obstacles to an efficient pdf solution in different applied examples. Therefore, besides the mentioned classical nonlinear Algorithm 1, in this paper, we present a linear approximation of the MaxEnt moment problem as Algorithm 2 using exponential Fup basis functions. Algorithm 2 solves the linear problem, satisfying only the proposed moments, using an optimal exponential tension parameter that maximizes Shannon entropy. Algorithm 2 is very efficient for larger numbers of moments and especially for skewed pdfs. Since both Algorithms have pros and cons, a hybrid strategy is proposed to combine their best approximation properties.

Download Full-text

Notes on Bell-Sejnowski PDF-Matching Neuron

Neural Computation ◽

10.1162/089976602760805304 ◽

2002 ◽

Vol 14 (12) ◽

pp. 2847-2855 ◽

Cited By ~ 3

Author(s):

Simone Fiori

Keyword(s):

Probability Density Function ◽

Probability Density ◽

Maximum Entropy ◽

Density Function ◽

Single Unit ◽

Neuron Model ◽

Maximum Entropy Principle ◽

Entropy Principle ◽

Single Input ◽

Pdf Matching

This article investigates the behavior of a single-input, single-unit neuron model of the Bell-Sejnowski class, which learn through the maximum-entropy principle, in order to understand its probability density function matching ability.

Download Full-text